Phase-encoded CSI spectroscopy using MRI is generally known and in wide use. Some examples of prior art MRI methods and apparatus (including methods for three-dimensional image construction) may be found, for example, in prior issued U.S. Pat. Nos. 4,297,637; 4,318,043; 4,471,305; and 4,599,565. The contents of these referenced related patents are hereby incorporated by reference.
The following documents provide background concerning MR spectroscopic imaging procedures and results:
Tropp et al, "Characterization of MR Spectroscopic Imaging of the Human Head and Limb at 2.0T.sup.1," 169 Radiology 207 (1988); and PA0 Ross et al, "Metabolic Response of Gioblastoma to Adoptive Immunotherapy: Detection by Phosphorus MR Spectroscopy," 13(2) Journal of Computer Assisted Tomography 189 (March/April 1989).
In the subject disclosure, the terms "CSI" (Chemical Shift Imaging) and "MRSI" (Magnetic Resonance Spectrographic Imaging) will be used interchangeably.
As is already well known in the art, a three-dimensional MRI data set may be created in a number of ways. For example, nuclear magnetic resonance RF data may be elicited from a plurality of parallel contiguous slice-volumes and phase encoded in two different dimensions (e.g., x,y) so that the NMR hydrogen and one (or more) other NMR sensitive nuclear density may be calculated for each volume element (voxel) within a given slice-volume using two-dimensional Fourier transform techniques. Another known technique obtains nuclear magnetic resonance RF spectral data from an entire three-dimensional volume including phase encoding in three dimensions (e.g., x,y,z) which then produces similar voxel spectral values for plural substantially parallel and contiguous slice-volumes three dimensions of Fourier transformation.
As is known by those in the art, Fourier transformation 16 from the phase-encoded "K space" to the spatial domain in which each voxel has associated with it a frequency waveform indicating a spectrum eliciting using well-known phase-encoded CSI spectroscopy techniques, as well as additional Fourier transformation from time to frequency domain.
Maintaining acceptable sensitivity and signal to noise ratio in a CSI spectroscopic system is a particularly critical and difficult problem (as those skilled in this art well know)--particularly when it is desired to view the spectrum of relatively small structures (e.g., lesions within the human body). This problem has been exacerbated in the past due to the essentially arbitrary position of the structure of interest with respect to the "grid" defined by the Fast Fourier transform (FFT). The exact position of the object to be imaged with respect to the imaging apparatus is not always capable of being precisely controlled. Thus, structures internal to the object (e.g., lesions and the like) generally do not fall entirely within a single "voxel" resolution element defined by the FFT function but instead may exist at the boundaries between two or more voxels (and thus fall within two or more voxels). The usual form of the FFT used is typically to evaluate the function of interest on grid points x.sub.k =K.lambda./N (where lambda is the field of view and N is the number of points transformed). This evaluation function provides a set of voxel boundaries for the spectroscopic image which may "skewer" lesions or other structures one would like to determine the composition of.
FIG. 1, for example, shows an exemplary lesion (or other small structure of interest) 10 within a larger body (not shown). Voxels 12a-12d are part of a 3-D "grid" defined by the FFT evaluation applied to the raw acquired data. The lesion 10 shown in this example is smaller than each of voxels 12 but happens to contain the intersection point 14 between eight voxels (this is perhaps a "worst case" situation for a structure which is small relative to voxel volume or even comparable in size to voxel volume, since only a small portion of the lesion is within any one voxel).
Lesion 10 thus has its total volume divided between eight different voxels 12 (only four of the eight voxels are shown in FIG. 1, with four other voxels being "closer" to the viewer to the left of the four voxels shown). Only a small portion 16a of lesion 10 is contained within voxel 12a, for example, and this portion 16a is very small relative to the total volume of voxel 12a. Each of the other voxels 12 containing a part of lesion 10 in the example shown likewise contains a volume of the lesion which is small relative to the total voxel volume.
The spectral data corresponding to voxel 12a, in the example shown, will have a component attributable to lesion portion 16a, but will reflect mostly the tissue adjacent to the lesion 10 which occupies the remainder of voxel 12a--and a similar situation applies for each of the other voxels containing other portions of the lesion. Thus, the spectrum of lesion 10 (or other structure of interest) which overlaps the boundaries of several voxels is "diluted" with the spectral characteristics of the surrounding tissue. This effect may cause the unique features of the lesion spectrum to be obscured or even lost entirely--thereby diluting any pathologic manifestations of the lesion with spectra from normal tissue adjacent to the lesion.
Others have already recognized that it is possible to use suitable phase shifts in the "k space", or "wavevector space" so as to effect spatial translational shifting of the voxel matrix array in the resulting three-dimensional image--and that such phase shifting can be provided by using Fourier transform techniques.
For example, the shift theorem as such has thus been applied to medical imaging to solve the problem of interpolation between planes of a three-dimensionally Fourier encoded spatial image. See Leifer et al "NMR Volume Imaging with Half Slice Offsets", Soc. Mag. Res. Med., Book of Abstracts, 4th Annual Meeting (August 19-23, 1985, Volume 1, pp 1013-1014).
Kaufman and Kramer (see referenced copending patent application above) have extended the range of the application of the shift theorem to allow facile viewing of oblique slices or even curved laminas. However, all these applications have a common thread: avoidance of the problems of interpolation between image points when a non-standard view is desired.
Messrs. Twieg et al ("An Improved Spectroscopic Imaging(SI) Technique for Localized Phosphorus NMR Spectroscopy; Direct Comparison of SI and ISIS in Human Organs," Soc. Mag. Res. Med., 7th Annual Meeting, August 20-26, 1988, Vol. 2) also mentioned that "spectra can be reconstructed from any number of individual volumes of interest (VOIs), at locations chosen after data acquisition." However, Twieg et al do not give any information at all as to how this process is to be effected (e.g., whether by various spatial domain interpolation techniques or frequency domain phase shifts, or some method distinct from either of these).
However, we have now ascertained that phase shifting in the K space may be utilized to shift the voxels in magnetic resonance spectroscopic images so as to translate them in (e.g., in two dimensions, such as x and y dimensions). Briefly, in accordance with one aspect of our invention, we locate the position of a structure of interest via conventional means (e.g., by generating a 1H "scout" image). We then apply the shift theorem for finite Fourier Transforms to shift voxel boundaries preferably in two (or more) dimensions so as to maximally enclose the lesion in a single voxel. Voxel shifts can be accomplished computationally by minimal manipulation of the raw data--and can thus be performed after the patient has left the imaging facility.
Thus, our application is quite different in motivation from those that have used the shift theorem in the past so as to avoid interpolation problems associated with non-standard views. Our desire is to ensure that the voxel boundaries in a spectroscopic image are placed so as to maximally or optimally enclose any lesion of interest, as located in a scout image. Our method is equally applicable for any phase encoded spectroscopic imaging experiment, regardless of whether one, two, or three dimensions of space encoding are employed.
Briefly, it is well known in information theory that a periodic signal with a high frequency cut off can be faithfully represented by a Fourier series with a finite number of terms. Therefore, a finite collection of Fourier coefficients suffices for the representation of a continuous function, which may be evaluated at any of an infinite number of points on a continuous domain. These considerations apply equally for signals in the time domain, where the Fourier transform is calculated in the frequency space; or for functions of space coordinates (e.g., images), where the transform is calculated in wave vector, or "k" space. Furthermore, they apply to objects with spatial extension in two or three dimensions.
For simplicity, we consider an example in one dimension: EQU f(x)=.SIGMA.F.sub.n exp(2.pi.inx/.lambda.) Equation 1
where the sum over n is from -N/2 to N/2-1, i.e., over a finite number of terms. Then the function can be obtained at any of an infinite number of values by changing the value of the variable x, while still using the same finite collection of Fourier coefficients, F.sub.n.
The advent of the Fast Fourier Transform (FFT), which relies exclusively on the finite Fourier transform, changes the ground rules for evaluating an expanded function at an arbitrary point, as follows. The expanded function is evaluated on a predetermined grid of points, which are obtained by dividing the field of view into an integral number of steps, including the end points. The number of points equals the number of coefficients, so (naively) the points at which the function can be evaluated ar irrevocably fixed. In fact, we have discovered that the limitation implied in the naive view can be overcome by an application of the shift theorem for Fourier transforms as applied to the finite transform. In naive terms, this is tantamount to shifting the grid of observation points by a small amount, so that the end points of the grid no longer coincide with the extremal points of the field of view.